相关论文: Counting isolated singularities in germs of applic…

Let $M$ be a two dimensional complex manifold, $p \in M $ and \Fl a germ of holomorphic foliation of \M at $p$. Let $S\subset M$ be a germ of an irreducible, possibly singular, curve at $p$ in $M$ which is a separatrix for \Fl. We prove…

Our recent extension of Arnold's classification includes all singularities of corank up to two equivalent to a germ with a non-degenerate Newton boundary, thus broadening the classification's scope significantly by a class which is…

In this note, we prove: \medskip \noindent {\bf Theorem A:} \emph{ There is a fixed constant $C$ such that for any positive integer $n$ and prime $p$, every finite subgroup $G$ of order coprime to $p$ of ${\rm GL}(n,\mathbb{C})$ has an…

The degree of a CSP instance is the maximum number of times that a variable may appear in the scope of constraints. We consider the approximate counting problem for Boolean CSPs with bounded-degree instances, for constraint languages…

We say that the the germ of a singular holomorphic foliation on $(\mathbb{C}^2,0)$ is algebraizable whenever it is holomorphically conjugate to the singularity of a foliation defined globally on a projective algebraic surface. The object of…

Let $M_n$ be an $n\times n$ random matrix with i.i.d. Bernoulli(p) entries. We show that there is a universal constant $C\geq 1$ such that, whenever $p$ and $n$ satisfy $C\log n/n\leq p\leq C^{-1}$, \begin{align*} {\mathbb…

We consider the parameterization ${\mathbf{f}}=(f_0,f_1,f_2)$ of a plane rational curve $C$ of degree $n$, and we want to study the singularities of $C$ via such parameterization. We do this by using the projection from the rational normal…

If $(\widetilde{X},E)\to (X,o)$ is the resolution of a complex normal surface singularity and $c_1:{\rm Pic}(\widetilde{X})\to H^2(\widetilde{X},{\mathbb Z})$ is the Chern class map, then ${\rm Pic}^{l'}(\widetilde{X}):= c_1^{-1}(l')$ has a…

Abstract. In this article, we provide an algorithm to compute the number of moduli of a germ of curve which is an union of germs of smooth curves in the complex plane.

The classical derangement numbers count fixed point-free permutations. In this paper we study the enumeration problem of generalized derangements, when some of the elements are restricted to be in distinct cycles in the cycle decomposition.…

Let $(X,C)$ be a germ of a threefold $X$ with terminal singularities along an irreducible reduced complete curve $C$ with a contraction $f: (X,C)\to (Z,o)$ such that $C=f^{-1}(o)_{red}$ and $-K_X$ is ample. Assume that $(X,C)$ contains a…

Let $(X, 0)$ be a complex analytic surface germ embedded in $(\mathbb{C}^n,0)$ with an isolated singularity and $\Phi=(g,f):(X,0) \longrightarrow (\mathbb{C}^2,0)$ be a finite morphism. We define a family of analytic invariants of the…

Applying Geometric Invariant Theory (GIT), we study the stability of foliations of degree 3 on P^2 with a unique singular point of multiplicity 1, 2, or 3 and Milnor number 13. In particular, we characterize those foliations for…

Let $\mathcal F$ be a holomorphic one-dimensional foliation on $\mathbb{P}^n$ such that the components of its singular locus $\Sigma$ are curves $C_i$ and points $p_j$. We determine the number of $p_j$, counted with multiplicities, in terms…

We provide a family of isolated tangent to the identity germs $f:(\mathbb{C}^3,0) \to (\mathbb{C}^3,0)$ which possess only degenerate characteristic directions, and for which the lift of $f$ to any modification (with suitable properties)…

Let $\mathcal{F}$ be a plane singular curve defined over a finite field $\mathbb{F}_q$. The linear system of plane curves of a given degree passing through the singularities of $\cF$ provides potentially good bounds for the number of points…

Let $\mathbb{G}$ be any Carnot group. We prove that if a convolution type singular integral associated with a $1$-dimensional Calder\'on-Zygmund kernel is $L^2$-bounded on horizontal lines, with uniform bounds, then it is bounded in $L^p, p…

We prove that there exists a constant $k$ with the property: if $\calC$ is a conjugacy class of a finite group $G$ such that every $k$ elements of $\calC$\ generate a solvable subgroup then $\calC$ generates a solvable subgroup. In…

Let X be a reduced complex-analytic germ of pure dimension n\ge2, with arbitrary singularities (not necessarily normal or complete intersection). Various homology cycles on Link_\ep[X] vanish at different speeds when \ep\to0. We give a…

We say that a subgroup $H$ is isolated in a group $G$ if for every $x\in G$ we have either $x\in H$ or $\langle x\rangle\cap H=1$. In this short note, we describe the set of isolated subgroups of a finite abelian group. The technique used…